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Kinematics and dynamics of a Cardan

This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode Galerkin discretization. Corresponding forced Mathieu-Duffing equation is solved by using the perturbation multiple time scales method for the weak nonlinearity and by the semi-numerical incremental harmonic balance method for the strongly nonlinear case. A comparison of the results from two methods is performed in the validation study for the weakly nonlinear case and a fine agreement is achieved. A parametric study is performed and the advantages and deficiencies of each method are discussed for order two and three superharmonic resonance conditions. The results demonstrate a significant influence of the fractional-order damping of the visco-Pasternak foundation as well as the nonlocal parameter and external excitation load on the frequency response of the system. The proposed methodology can be used in pre-design procedures of novel energy harvesting and sensor devices at small scales exhibiting nonlinear dynamic behavior.

Inerter devices are used in Formula 1 vehicles for a decade to reduce vertical and rolling displacement at the corner of the sharp racing curves and provide higher tire grip on racing challenges. To improve dynamics Formula SAE Car, several topological designs for suspension system are already proposed and published [1]. Based on our passive suspension system for quarter-car model, we carried out analysis for different parameters and under the impact from the road disturbance and demonstrated when integrated inerter device can increase ride comfort and decrease vertical displacement. Proposed solution system with integrated inerter mechanism can improve vehicle suspension systems development and have effects on dynamics and stability of a vehicle.

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